A bstract It is expected that when the string coupling is taken to be sufficiently small, a black hole turns into a bound state of self-gravitating fundamental strings. This state would be described by winding strings wrapping around the Euclidean time circle, known as the Horowitz-Polchinski solution. In this paper, we study such a self-gravitating string configuration in two-dimensional dilaton gravity theories. We first derive an analytic expression of the solution describing a winding string in two-dimensions and investigate in detail the geometry of this solution. Our winding string solution in two dimensions describes the geometry near the surface of the bound state of self-gravitating strings in the large-dimension limit, much like a two-dimensional black hole describes the near horizon geometry of the Schwarzschild black hole in the large-dimension limit. To study quantum effects around self-gravitating strings, we obtain an analytic solution of winding strings in the RST model. In a similar fashion to the Hartle-Hawking vacuum around a black hole, our string solution in the RST model contains the background radiation, whose temperature is the same as that of the winding strings.
Ishibashi et al. (Mon,) studied this question.